DIRICHLET FORMS AND ULTRAMETRIC CANTOR SETS ASSOCIATED TO HIGHER-RANK GRAPHS

DOI10.1017/S1446788719000429zbMath1475.46063arXiv1808.09227OpenAlexW2999745570MaRDI QIDQ4983574

Sooran Kang, Jaeseong Heo, Yongdo Lim

Publication date: 26 April 2021

Published in: Journal of the Australian Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1808.09227

zbMATH Keywords

Dirichlet formsheat kernelsasymptotic behaviorsultrametric Cantor sets\(k\)-graphs\(k\)-Bratteli diagrams

Mathematics Subject Classification ID

Noncommutative differential geometry (46L87) Jump processes on discrete state spaces (60J74)

Related Items (1)

\(K\)-theory for real \(k\)-graph \(C^\ast\)-algebras

Cites Work

• Cuntz-Krieger algebras and wavelets on fractals
• Transverse Laplacians for substitution tilings
• Analysis of orthogonality and of orbits in affine iterated function systems
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• Dirichlet forms and symmetric Markov processes
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• Spectral triples and wavelets for higher-rank graphs
• KMS states on the \(C^\ast\)-algebra of a higher-rank graph and periodicity in the path space
• UCT-Kirchberg algebras have nuclear dimension one
• Noncommutative Riemannian geometry and diffusion on ultrametric Cantor sets
• The primitive ideals of the Cuntz-Krieger algebra of a row-finite higher-rank graph with no sources
• Heat kernel estimates for jump processes of mixed types on metric measure spaces
• On the \(K\)-theory of higher rank graph \(C^*\)-algebras
• Representations of Cuntz-Krieger relations, dynamics on Bratteli diagrams, and path-space measures
• Periodicity in Rank 2 Graph Algebras
• Monic representations of finite higher-rank graphs
• Wavelets and spectral triples for fractal representations of Cuntz algebras
• Branching laws for endomorphisms of fermions and the Cuntz algebra O2

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